Magnetic flow of viscous gas between rotating surfaces of revolution

In this work the steady laminar magnetic flow of viscous gas is considered in a narrow space (slot) between two surfaces of revolution rotating with constant angular velocities around a common axis of symmetry. The linearised equations of magnetic motion of the viscous gas flow for axial symmetry in the intrinsic curvilinear orthogonal coordinate system $\text{x, φ, y}$ are used. The obtained solutions of the equations of motion have been illustrated by examples of gas flow through the slot of constant thickness between rotating and fixed conical surfaces, and between rotating and fixed spherical surfaces.     

Elastodynamic near-tip fields for a rapidly propagating interface crack

The elastodynamic stress field near a crack tip rapidly propagating along the interface between two dissimilar isotropic elastic solids is investigated. Both anti-plane and in-plane motions are considered. The anti-plane displacements and the in-plane displacement potentials are sought in the separated forms $\text{r}{}^{\mathrm{q}}\text{F(θ)}$, $\text{r}$ and θ being polar coordinates centered at the moving tip. The mathematical statement of the problem reduces to a second-order linear ordinary differential equation in θ, which can be solved analytically. Formulation of the boundary and interface conditions leads to an eigenvalue problem for the singularity exponent $\text{q}$. For the in-plane problem, root $\text{q}$ is found to be complex. Thus, the stresses exhibit violent oscillations within a small region around the crack tip, and the solutions have physical significance only outside this region. The angular stress distributions are plotted for various crack speeds, and it is found that at a high enough speeds the direction θ of maximum stress moves out of the interface. This result indicates that a running interface crack may move into one of the adjoining materials.     

Heat transfer and flow instability in a superconducting machine rotating at 3000 rpm

Heat transfer measurements have been carried out on the liquid He⁴ in a side arm rotating at a speed of 3000 rpm. The heat transfer cell consists of a copper disc mounted perpendicularly to the radial direction at a radial distance of 0.41 m. A correlation of the type: $\text{Nu/(1 + S}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{)}\text{= 0.17}\text{R}{}_{\mathrm{a}}{}^{0.3}$ where S is the stratification factor, has been obtained.The flow pattern of He⁴-gas through a U-tube under a self-pumping system in a rotating frame has been studied analytically. It can be demonstrated that the flow polarity is influenced by the velocity gradient of the friction factor in the region, between stream-line and turbulent motions, which can lead to flow instability of the kind observed experimentally recently. It has been explained that the instability may occur in both increasing and decreasing speed modes or heat inputs.     

Periodic distributions of inclusions

Elastic fields caused by periodically distributed spherical inclusions in an infinite isotropic medium are investigated when eigenstrains in the inclusions are homogeneous polynomials of degree $\text{l}$ of the local coordinates taken at the centers of the inclusions. The stress field can be expressed as a convergent sum of the solutions of individual inclusions when $\text{l}$ is an odd number. The stress field must be modified when $\text{l}$ is an even number. If a distribution of inclusions is on a plane or a line, the stress field can be expressed as a convergent sum of the individual inclusions for all $\text{l}$. The analysis is extended to general ellipsoidal inclusions with arbitrary eigenstrains in anisotropic media.     

Structure helimagnetique de NaMnCrF6

In NaMnCrF₆ the three magnetic sublattices Cr₁, Cr₂ and Mn order below 21K. The propagation vector $\text{q}\text{= (0, 0, 0.018)}$ implies a very large magnetic unit-cell ($\text{? 278}$ A along $\text{c}$). The configuration of the moments is helical and generated by rotating a ferrimagnetic colinear mode in an oblique plane.     

Analysis of incremental cracking by the stress-wave emission technique

One of the most fruitful areas for application of the acoustic emission technique lies in characterization of yielding and fracture processes. For example, what are the microscopic details of the macroscopic slow crack growth process that precedes crack instability? Fundamental to answering this is the ability to detect and quantify the microcracking phenomena. It was found that the emission of a single elastic stress wave could be correlated to a load drop, ΔP, occuring during crack growth. Furthermore, this load drop could be interpreted via a theoretical compliance analysis in terms of area swept out by the advancing crack. It is proposed that any discrete stress wave emission associated with a fracture process can be interpreted in terms of an incremental fracture area, ΔA. This is given by

$\text{g=}\text{2·5 m K W}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{δA}\text{YLB}$

where g is the amplitude of the emission. K is the applied stress intensity, L is the distance between grips, W is the specimen width, B is the specimen thickness. Y is f(a/w) and m is the proportionality constant between stress wave amplitude and $\text{ΔP}\text{B}$. Crack-line loaded or compact tension specimens of 7075-T6 aluminum were used for the experimental investigation. A theoretical relationship between the load drop and the crack growth step was derived for this test specimen configuration. Over fifty experimental observations verified the linear relationship between g and $\text{ΔP}\text{B}$. For the above relationship, m was found to be 0.05 in²/lb sec² from the compact tension data.     

Interrelation of crack opening displacement and J-integral

The relationship between $\text{J-}\text{integral}$ and crack opening displacement δ is based on theoretical as well as experimental investigations and is of the general form $\text{J = Mσ}{}_{\mathrm{r\delta }}$. The significance of M and its possible dependence on specimen geometry and material properties is unknown. An attempt is made in the present paper to identify the different variables and to account for them in $\text{H-δ}$ relationship. It is observed that if the material properties remain constant, $\text{M}$ increases with $\text{a/W}$ ratio upto 0.5 and then probably decreases for higher $\text{a/W}$ ratios. If the specimen geometry and size is maintained constant then it is observed that $\text{M}$ increases with decreasing yield strength and a corresponding increase in work hardening exponent.     

On a lagrangean action based kinetic instability theorem of Kelvin and Tait

This article provides a simple and comprehensive proof of the Kelvin/Tait Kinetic Instability theorem. According to it: “if the Lagrangean Action (LA) of a holonomic and conservative system along a fundamental trajectory $\text{I}$ for cotermini and noncontemporaneous but isoenergetic variations $\text{}\text{̂}\text{gd(I)}$, is a minimum, when calculated from an initial configuration to a final one reached at any time, however much later, then $\text{I}$ is unstable”. The proof hinges on the study of the sign of the second such variation $\text{}\text{̂}\text{gd}{}^2\text{(LA)}$, of $\text{LA}$. The introduction of the concept of Lagrangean kinetic foci, combined with the extended Jacobi's sufficiency condition (for this variable endpoints variational problem) leads to a hitherto missing quantitative formulation of the theorem. Possible extensions to nonconservative systems are also indicated.     

Fatigue crack propagation behaviour of rotor and wheel materials used in steam turbines

The fatigue crack propagation characteristics of several rotor and wheel materials that are commonly used in rotating components of steam turbines were investigated. Particular emphasis was placed on the behaviour at near-threshold growth rates, ie below 10^?5 mm/cycle, approaching the fatigue-crack propagation threshold, $\text{ΔK}{}_{\mathrm{<mtext>th</mtext>}}$. The lifetimes of the cracks of interest lie mostly in this region, and it is also the region where few data are available.The effects of load ratio on the fatigue crack growth rates were examined, as well as the tensile, Charpy V-notch and fracture toughness properties of the rotor and wheel materials. The relationship between fatigue crack propagation behaviour and fractographic features was examined. Fatigue crack growth rate data, $\text{da/d}\text{N}$ vs stress intesity range $\text{ΔK}$, were fitted with a four parameter Weibull survivorship function. This curve fitting can be used for life estimation and establishment of $\text{ΔK}{}_{\mathrm{<mtext>th</mtext>}}$. The results show that load ratio and microstructure play a role in determining the fatigue crack threshold and fatigue crack growth behaviour.     

Condensation and epitaxial growth of K on W(001)

The growth of K layers on W(001) from the first adsorption phases up to the deposition of thick films has been investigated by means of a RHEED camera, in the temperature range 143 ? T ? 273 K. At first the deposited potassium atoms form a W(001)-c(2 × 2)K⁺ structure, upon which a non-ionized but polarized adstructure grows. Further condensation is characterized by a very low binding energy of 0.09 eV to the substrate layer and consequently by a low condensation coefficient. The transition layer grows out of single adsorption events without the formation of nuclei, while the epitaxial layers growing upon it are initiated by three-dimensional nucleation. For these layers, epitaxial orientations $\text{K}\text{(001)}\text{W}\text{(001)}\text{with}\text{K}\text{[001]}\text{W}\text{[010]}$ or $\text{K}\text{[001]}\text{W}\text{[100]}$ were observed.     

Asymptotic analysis of the torsional modes of wave propagation in a piezoelectric solid circular cylinder of (622) class

An asymptotic method due to “Achenbach” is used to analyze the torsional modes of wave propagation in a solid circular cylinder of piezoelectric material of (622) crystal class. Information obtained in this method is useful for the frequency spectrum at long wavelengths. In this method, the field variables and the frequency are expressed as power series of the dimensionless wavenumber, $\text{? = 2π × R/W}$. Substituting these expansions in the field equations and the boundary conditions, a system of coupled second order inhomogeneous ordinary differential equations with the radial coordinate as independent variable is obtained by collecting the terms of same order $\text{?}{}^{\mathrm{m}}$. Integration of such systems of differential equations yield the various terms in the series expansions for the above modes and for the whole range of frequencies, when the real-valued dimensionless wavenumber less than unity ($\text{0<?<1}$). To test the correctness of the present scheme, the roots of the exact frequency equation are computed in double precision and the results thus obtained are compared with the results obtained in the present analysis. The results agree upto five decimal places.     

Unsteady hydromagnetic couette flow in a rotating system

Unsteady hydromagnetic flow of an electrically conducting viscous incompressible fluid in a rotating system under the influence of a uniform transverse magnetic field is investigated when one of the plates is set into motion with the time dependent velocity $\text{U(t)}$ in its own plane. Two cases of interest, namely, impulsive start as well as accelerated start of the moving plate are discussed. The asymptotic behaviour of the solution is also analysed for both small and large time to highlight the transient approach to the final steady state and effects of rotation parameter as well as Hartmann number. The shear stresses at the moving plate due to the primary and secondary flows are derived in both cases. It is found that the shear stress components due to the primary flow decrease, whereas that due to the secondary flow increase with the increase in rotation parameter.     

(W4O16)8− Polyion in the high temperature modification of silver tungstate

The high temperature form of silver tungstate, Ag₈W₄O₁₆, contains tetratungstate ions in which the tungsten atoms are coplanar and each is octahedrally coordinated to oxygen atoms. Two octahedra share three edges with other octahedra and two octahedra share two edges with other octahedra. Four types of coordination for the Ag⁺ ion are found in the structure: distorted triangular prismatic (with an additional more distant oxygen through a quadrilateral face), octahedral, tetrahedral, and twofold linear. These have been observed before in different crystals, but not all in the same crystal. The deviation from centrosymmetry of the polyion appears to be highly stable as deduced from unsuccessful attempts to reverse the polarization of the crystal.Crystals of Ag₈W₄O₁₆ are orthorhombic, belong to space group Pn2n (C¹⁰_2v) with lattice constants a=10.89, b=12.03, $\text{c}\text{=5.92}\text{A}\text{?}$ all $\text{±0.02}\text{A}\text{?}$ and contain 2 Ag₈W₄O₁₆ per unit cell. X-ray diffraction data obtained with a Buerger-Supper single crystal automatic diffractometer were used to determine the crystal structure.     

The systematic construction of liapunov functionals in the linear stability of conservative steady flows

The linearized equations of motion for small perturbations about a state of steady flow of a conservative dynamical system, when expressed in appropriate variables, admit a class of explicit constants of motion. The construction of Liapunov functionals from these constants of motion is discussed, with applications to plane parallel flow of an inviscid incompressible fluid and plane parallel flow of an inviscid, compressible, electrically charged fluid. Bounds on the $\text{L}{}_2\text{-}\text{norms}$ of certain system variables are obtained.     

A note on the temperature dependence of the normal stress moduli

In this analysis we establish necessary and sufficient conditions which the normal stress modulus $\text{α}{}_1\text{(θ)}$ and its derivative $\text{dα}{}_1\text{(θ)/dθ}$ ought to satisfy if a homogeneous incompressible second grade fluid is to meet the requirement that the specific internal energy of the fluid be a minimum when the fluid is locally at rest. We also require that all arbitrary motions of the fluid meet the Clausius-Duhem inequality. It is found that requiring that the specific internal energy of the fluid be a minimum when the fluid is locally at rest is not equivalent to a similar requirement on the specific Helmholtz free energy.     

Approximate Mode II velocity correction factors for 90° unidirectional fiber composites

A static Mode III isotropic/Mode II orthotropic analogy is developed for 90° highly orthotropic fiber composites. This static analogy is extended to the dynamic regime and the velocity correction factors for the dynamic energy release rate and the dynamic stress intensity factor are obtained for the Mode II case. The complete dynamic analogies are given. The approximate Mode II 90° velocity correction factors $\text{W}{}_{\mathrm{II(90°)}}$ and $\text{S}{}_{\mathrm{II((90°)}}$ are of the same general form as the approximate Mode I velocity correction factors, $\text{W}{}_{\mathrm{I(0°)}}$, $\text{W}{}_{\mathrm{I(90°)}}$, $\text{S}{}_{\mathrm{I(0°)}}$ and $\text{S}{}_{\mathrm{I(90°)}}$ Whereas the four Mode I velocity correction factors approach zero as the crack-tip velocity approaches the composite shear wave speed, $\text{w}{}_{\mathrm{II(90°)}}$ and $\text{s}{}_{\mathrm{II(90°)}}$ approach zero as the crack-tip velocity approaches the larger extensional wave speed.